Asymptotics of least squares for nonlinear harmonic regression

Abstract

This paper considers the least-squares estimator of a nonlinear regression problem where the regression function is a sum of sinusoids with unknown amplitudes and frequencies. It provides a complete proof of the consistency and the asymptotic normality of the nonlinear least-squares estimator after an expository discussion on the gaps and flaws in the related literature. © 2011 Taylor & Francis.